{"paper":{"title":"Optimal Weighted Smoothing and Asymptotics of Ancient Solutions for Fast Diffusion Equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hua-Yang Wang, Jingang Xiong, Xiqin Jiang","submitted_at":"2026-05-14T09:38:11Z","abstract_excerpt":"We establish sharp weighted smoothing estimates for limit solutions to the Cauchy-Dirichlet problem for the fast diffusion equation on smooth bounded domains.\n  We demonstrate that the critical exponent governing these estimates coincides with the classical Brezis--Turner exponent known in the theory of semilinear elliptic equations.\n  As a primary application, we derive improved global Harnack inequalities and describe asymptotic behavior of positive ancient solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14622","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}